Skip to main content

Gene Regulatory Models for Plant Development and Evolution

  • Chapter
  • First Online:
Plant Developmental Biology - Biotechnological Perspectives

Abstract

We argue for the need of mathematical models as integrative tools for understanding processes of cell differentiation and morphogenesis, involving the concerted action of multiple components at different spatiotemporal scales during plant development. We propose dynamical models of gene regulatory networks (GRNs) as the basis for such means. Such models enable the identification of specific steady-state gene expression patterns (attractors), which correspond to different cell types. A comparison between discrete and continuous models is then presented, and we propose that the dynamical structure of a GRN subject to noise conceptually corresponds to Waddington's “epigenetic landscape”. In the third section, we review methods to infer GRN topology from microarray experiments. These include reverse engineering techniques such as Bayesian networks, mutual information, and continuous analysis models. We discuss the application of these approaches to plant cases. However, detailed molecular biology experiments have been very successful in deciphering the structure of underlying small networks. Therefore, we then focus our attention on GRN models of such small modules for various processes of plant development. The first example corresponds to a single-cell GRN for primordial cell specification during early stages of Arabidopsis thaliana flower development. Then, some examples of coupled GRN dynamics in spatiotemporal domains are recalled: cell differentiation in A. thaliana leaf and root epidermis, and the spatiotemporal pattern of genes responsible for the apical shoot meristem behavior. Furthermore, we consider models on auxin transport mechanisms that are sufficient to generate observed morphogenetic shoot and root patterns. We also present several approaches to model signal transduction pathways that consider crosstalk among several biochemical pathways, as well as the influence of environmental factors. In Section 1.5 we consider the constructive role of noise in pattern formation in complex systems. We finally conclude that studies on GRN structure and dynamics aid at understanding evolutionary morphological patterns.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 189.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 249.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 249.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • Aguda BD, Goryachev AB (2007) From pathways databases to network models of switching behavior. PLoS Comput Biol 3:e152

    Article  Google Scholar 

  • Albert R, Othmer HG (2002) The topology of the regulatory interactions predicts the expression pattern of the segment polarity genes in Drosophila melanogaster. J Theor Biol 223:1–18

    Article  Google Scholar 

  • Aldana M, Balleza E, Kauffman S, Resendis O (2007) Robustness and evolvability in gene regulatory networks. J Theor Biol 245:433–448

    Article  PubMed  Google Scholar 

  • Alvarez-Buylla RE, Benítez M, Chaos A, Espinosa-Soto C, Padilla-Longoria P, Balleza E (2007) Gene regulatory network models for plant development. Curr Opin Plant Biol 10:83–91

    Article  PubMed  CAS  Google Scholar 

  • Andrec M, Kholodenko BN, Levy RM, Sontag E (2005) Inference of signaling and gene regulatory networks by steady-state perturbation experiments: structure and accuracy. J Theor Biol 232:427–441

    PubMed  CAS  Google Scholar 

  • Arenas A, Díaz-Guilera A, Pérez-Vicente C (2006) Synchronization reveals topological scales in complex networks. Phys Rev Lett 96:114102

    Article  PubMed  Google Scholar 

  • Arkin A, Ross J, McAdams HH (1998) Stochastic kinetic analysis of developmental pathway bifurcation in phage-infected Escherichia coli cells. Genetics 149:1633–1648

    PubMed  CAS  Google Scholar 

  • Benítez M, Espinosa-Soto C, Padilla-Longoria P, Díaz J, Alvarez-Buylla ER (2007) Equivalent genetic regulatory networks in different contexts recover contrasting spatial cell patterns that resemble those in Arabidopsis root and leaf epidermis: a dynamic model. Int J Dev Biol 51:139–155

    Article  PubMed  Google Scholar 

  • Benzi R, Sutera A, Vulpiani A (1981) The mechanism of stochastic resonance. J Phys A 14:L453–L457

    Article  Google Scholar 

  • Blake WJ, Kaern M, Cantor CR, Collins JJ (2003) Noise in eukaryotic gene expression. Nature 422:633–637

    Article  PubMed  CAS  Google Scholar 

  • Bower JM, Bolouri H (2001) Computational modeling of genetic and biochemical networks. MIT Press, Cambridge, MA

    Google Scholar 

  • Buck-Sorlin G, Hemmerling R, Kniemeyer O, Burema B, Kurth W (2008) A rule-based model of barley morphogenesis, with special respect to shading and gibberellic acid signal transduction. Ann Bot 110:1109–1123

    Google Scholar 

  • Cai L, Friedman N, Xie XS (2006) Stochastic protein expression in individual cells at the single molecule level. Nature 440:358–362

    Article  PubMed  CAS  Google Scholar 

  • Chaos A, Aldana M, Espinosa-Soto C, García Ponce de León B, Garay A, Alvarez-Buylla ER (2006) From genes to flower patterns and evolution: dynamic models of gene regulatory networks. J Plant Growth Regul 25:278–289

    Article  CAS  Google Scholar 

  • Cho KH, Kim JR, Baek S, Choi HS, Choo SM (2006) Inferring biomolecular regulatory networks from phase portraits of time-series expression profiles. FEBS Lett 580:3511–3518

    Article  PubMed  CAS  Google Scholar 

  • Coen E, Meyerowitz E (1991) The war of the whorls: genetic interactions controlling flower development. Nature 353:31–37

    Article  PubMed  CAS  Google Scholar 

  • Davidich MI, Bornholdt S (2008) Bolean network model predicts cell cycle sequence of fission yeast. PLoS ONE 3:e1672

    Article  PubMed  Google Scholar 

  • Davidson EH, Rast JP, Oliveri P, Ransick A, Calestani C, Yuh C-H, Minokawa T, Amore G, Hinman V, Arenas-Mena C, Otim O, Titus Brown C, Livi CB, Lee PY, Revilla R, Rust AG, Pan ZJ, Schilstra MJ, Clarke PJC, Arnone MI, Rowen L, Cameron RA, McClay DR, Hood L, Bolouri H (2002) A genomic regulatory network for development. Science 295:1669–1678

    Article  PubMed  CAS  Google Scholar 

  • Díaz J, Alvarez-Buylla ER (2006) A model of the ethylene signaling pathway and its gene response in Arabidopsis thaliana: pathway cross-talk and noise-filtering properties. Chaos 16:023112. doi:10.1063/1.2189974

    Article  PubMed  Google Scholar 

  • Dupuy L, Mackenzie J, Rudge T, Haseloff J (2008) A system for modelling cell cell interactions during plant morphogenesis. Ann Bot 101:1255–1265

    Article  PubMed  Google Scholar 

  • Espinosa-Soto C, Padilla-Longoria P, Alvarez-Buylla ER (2004) A gene regulatory network model for cell-fate determination during Arabidopsis thaliana flower development that is robust and recovers experimental gene expression profiles. Plant Cell 16:2923–2939

    Article  PubMed  CAS  Google Scholar 

  • Gammaitoni L, Hanggi P, Jung P, Marchesoni F (1998) Stochastic resonance. Rev Mod Phys 70:223–287

    Article  CAS  Google Scholar 

  • Gang H, Ditzinger T, Ning CZ, Haken H (1993) Stochastic resonance without external periodic force. Phys Rev Lett 71:807–810

    Article  PubMed  Google Scholar 

  • Grieneisen VA, Xu J, Maree1 AFM, Hogeweg P, Scheres S (2007) Auxin transport is sufficient to generate a maximum and gradient guiding root growth. Nature 449:1008–1013

    Article  PubMed  CAS  Google Scholar 

  • Hasty J, McMillen D, Isaacs F, Collins JJ (2001) Computational studies of gene regulatory networks: in numero molecular biology. Nature Rev Genet 2:268–279

    Article  PubMed  CAS  Google Scholar 

  • Holloway DM, Harrison LG (2007) Pattern selection in plants: coupling chemical dynamics to surface growth in three dimensions. Ann Bot 101:361–374

    Article  PubMed  Google Scholar 

  • Huang S, Ingber DE (2000) Shape-dependent control of cell growth, differentiation, and apoptosis: switching between attractors in cell regulatory networks. Exp Cell Res 262:91–103

    Article  Google Scholar 

  • Huang S, Ingber DE (2007) A non-genetic basis for cancer progression and metastasis: self-organizing attractors in cell regulatory networks. Breast Dis 26:27–54

    Google Scholar 

  • Huang S, Eichler G, Bar-Yam Y, Ingber DE (2005) Cell fates as high-dimensional attractor states of a complex gene regulatory network. Phys Rev Lett 94 128701

    Article  PubMed  Google Scholar 

  • Imoto S, Sunyong K, Goto T, Aburatani S, Tashiro K, Kuhara S, Miyano S (2002) Bayesian network and nonparametric heteroscedastic regression for nonlinear modeling of genetic network. In: Proc IEEE Computer Society Bioinformatics Conf, Palo Alto, CA, pp 219–227

    Google Scholar 

  • Irons DJ, Monk NAM (2007) Identifying dynamical modules from genetic regulatory systems: applications to the segment polarity network. BMC Bioinform 8:413. doi:10.1186/1471-2105-8-413

    Article  Google Scholar 

  • Jönsson H, Heisler M, Reddy GV, Agrawal V, Gor V, Shapiro BE, Mjolsness E, Meyerowitz EM (2005) Modeling the organization of the WUSCHEL expression domain in the shoot apical meristem. Bioinformatics 21 (Suppl 1):i232–i240

    Article  PubMed  Google Scholar 

  • Jönsson H, Heisler MG, Shapiro BE, Meyerowitz EM, Mjolsness E (2006) An auxin-driven polarized transport model for phyllotaxis. Proc Natl Acad Sci USA 103:1633–1638

    Article  PubMed  Google Scholar 

  • Kaneko K (1998) On the strength of attractors in a high-dimensional system: Milnor attractor network, robust global attraction, and noise-induced selection. Physics D 124:322–344

    Article  Google Scholar 

  • Kashtan N, Alon U (2005) Spontaneous evolution of modularity and network motifs. Proc Natl Acad Sci USA 102:13773–13778

    Article  PubMed  CAS  Google Scholar 

  • Kauffman S (1969) Metabolic stability and epigenesis in randomly constructed genetic nets. J Theor Biol 22:437–467

    Article  PubMed  CAS  Google Scholar 

  • Kholodenko BN, Kiyatkin A, Bruggeman FJ, Sontag E, Westerhoff HV, Hoek JB (2002) Untangling the wires: a strategy to trace functional interactions in signaling and gene networks. Proc Natl Acad Sci USA 99:12841–12846

    Article  PubMed  CAS  Google Scholar 

  • Kim SY, Imoto S, Miyano S (2003) Inferring gene networks from time series microarray data using dynamic Bayesian networks. Brief Bioinform 4:228–235

    Article  PubMed  CAS  Google Scholar 

  • Kraut S, Feudel U, Grebogi C (1999) Preference of attractors in noisy multistable systems. Phys Rev E 59:5253–5260

    Article  CAS  Google Scholar 

  • Levine M, Tjian R (2003) Transcription regulation and animal diversity. Nature 424:147–151

    Article  PubMed  CAS  Google Scholar 

  • Li W, Graur D (1991) Fundamentals of molecular evolution. Sinauer Press, Sunderland, MA

    Google Scholar 

  • Li S, Assmann SM, Albert R (2006) Predicting essential components of signal transduction networks: a dynamic model of guard cell abscisic acid signaling. PLoS Biol 4:e312

    Article  PubMed  Google Scholar 

  • Margulis L, Sagan D (1986) Microcosmos. Summit Books, New York

    Google Scholar 

  • Mendoza L, Alvarez-Buylla ER (1998) Dynamics of the genetic regulatory network for Arabidopsis thaliana flower morphogenesis. J Theor Biol 193:307–319

    Article  PubMed  CAS  Google Scholar 

  • Mendoza L, Alvarez-Buylla ER (2000) Genetic regulation of root hair development in Arabidopsis thaliana: a network model. J Theor Biol 204:311–326

    Article  PubMed  CAS  Google Scholar 

  • Mendoza L, Thieffry D, Alvarez-Buylla ER (1999) Genetic control of flower morphogenesis in Arabidopsis thaliana: a logical analysis. Bioinformatics 15:593–606

    Article  PubMed  CAS  Google Scholar 

  • Milo R, Itzkovitz S, Kashtan N, Levitt R, Shen-Orr S, Ayzenshtat I, Sheffer M, Alon U (2004) Superfamilies of evolved and designed networks. Science 5663:1538–1542

    Article  Google Scholar 

  • Mjolsness E, Sharp DH, Reinitz J (1991) A connectionist model of development. J Theor Biol 152:429–454

    Article  PubMed  CAS  Google Scholar 

  • Nicolis C (1981) Solar variability and stochastic effects on climate. Sol Phys 74:473–478

    Article  Google Scholar 

  • Nicolis C (1982) Stochastic aspect of climatic transitions-response to a periodic forcing. Tellus 34:1–9

    Article  Google Scholar 

  • Paulsson J (2004) Summing up the noise in gene networks. Nature 427:415–418

    Article  PubMed  CAS  Google Scholar 

  • Paulsson J, Berg OG, Ehrenberg M (2000) Stochastic focusing: fluctuation-enhanced sensitivity of intracellular regulation. Proc Natl Acad Sci USA 97:7148–7153

    Article  PubMed  CAS  Google Scholar 

  • Pesch M, Hülskamp M (2004) Creating a two-dimensional pattern de novo during Arabidopsis trichome and root hair initiation. Curr Opin Genet Dev 14:422–427

    Article  PubMed  CAS  Google Scholar 

  • Pikovsky AS, Kurths J (1997) Coherence resonance in a noise-driven excitable system. Phys Rev Lett 78:775–778

    Article  CAS  Google Scholar 

  • Quayle AP, Bullock S (2006) Modelling the evolution of genetic regulatory networks. J Theor Biol 238:737–753

    Article  PubMed  CAS  Google Scholar 

  • Rao CV, Wolf DM, Arkin AP (2002) Control, exploitation and tolerance of intracellular noise. Nature 420:231–237

    Article  PubMed  CAS  Google Scholar 

  • Ravasz E, Somera AL, Mongru DA, Oltvai ZN, Barabasi AL (2002) Hierarchical organization of modularity in metabolic networks. Science 297:1551–1555

    Article  PubMed  CAS  Google Scholar 

  • Rudall P (1987) Anatomy of flowering plants. An introduction to structure and development. Edward Arnold, London

    Google Scholar 

  • Russell DF, Wilkens LA, Moss F (1999) Use of behavioural stochastic resonance by paddle fish for feeding. Nature 402:291–294

    Article  PubMed  CAS  Google Scholar 

  • Rustici G, Mata J, Kivinen K, Lió P, Penkett CJ, Burns G, Hayles J, Brazima A, Nurse P, Bähler J (2004) Periodic gene expression program of the fission yeast cell cycle. Nature Genet 36:809–817

    Article  PubMed  CAS  Google Scholar 

  • Savage NS, Schmidt W (2008) From priming to plasticity: the changing fate of rhizodermic cells. BioEssays 30:75–81

    Article  PubMed  Google Scholar 

  • Scheres B (2001) Plant cell identity. The role of position and lineage. Plant Physiol 125:112–114

    Article  PubMed  CAS  Google Scholar 

  • Siegal ML Promislow DEL, Bergman A (2007) Functional and evolutionary inference in gene networks: does topology matter? Genetica 129:83–103

    Article  PubMed  CAS  Google Scholar 

  • Smolen P, Baxter DA, Byrne JH (2000) Modeling transcriptional control in gene networks – methods, recent results, and future directions. Bull Math Biol 62:247–292

    Article  PubMed  CAS  Google Scholar 

  • Solé R, Valverde S (2006) Are network motifs the spandrels of cellular complexity? Trends Ecol Evol 21:419–422

    Article  PubMed  Google Scholar 

  • Sontag E, Kiyatkin A, Kholodenko BN (2004) Inferring dynamic architecture of cellular networks using time series of gene expression, protein and metabolite data. Bioinformatics 20:1877–1886

    Article  PubMed  CAS  Google Scholar 

  • Steuer R, Kurths J, Daub CO, Weise J, Selbig J (2002) The mutual information: detecting and evaluating dependencies between variables. Bioinformatics 18:S231–S240

    PubMed  Google Scholar 

  • Vieten A, Sauer M, Brewer PB, Friml J (2007) Molecular and cellular aspects of auxin-transport-mediated development. Trends Plant Sci 12:160–168

    Article  PubMed  CAS  Google Scholar 

  • Vilar JMG, Guet CC, Leibler S (2003) Modeling network dynamics: the lac operon, a case study. J Cell Biol 161:471–476

    Article  PubMed  CAS  Google Scholar 

  • Waddington CH (1957) The strategy of the genes. Geo Allen & Unwin, London

    Google Scholar 

  • Wang Z, Zhang J (2007) In search of the biological significance of modular structures in protein networks. PLoS Comput Biol 3:e107. doi:10.1371/journal.pcbi.0030107

    Article  PubMed  Google Scholar 

  • Wang Z, Hou Z, Xin H, Zhang Z (2007) Engineered internal noise stochastic resonator in gene network: a model study. Biophys Chem 125:281–285

    Article  PubMed  CAS  Google Scholar 

  • Whitfield ML, Sherlock G, Saldanha AJ, Murray JI, Ball CA, Alexander KE, Matese JC, Perou CM, Hurt MM, Brown PO, Botstein D (1992) Identification of the genes periodically expressed in the human cell cycle and their expression in tumors. Mol Biol Cell 13:1977–2000

    Article  Google Scholar 

Download references

Acknowledgements

Financial support was from the Programa de Apoyo a Proyectos de Investigación e Innovación Tecnológica, Universidad Nacional Autónoma de México IN230002 and IX207104, and Consejo Nacional de Ciencia y Tecnología CO1.41848/A-1, CO1.0538/A-1 and CO1.0435.B-1 grants to E.A.B., and PhD and postdoctoral scholarships from the Consejo Nacional de Ciencia y Tecnología and Universidad Nacional Autónoma de México to A.C.C. and M.B.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to E. R. Alvarez-Buylla .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Alvarez-Buylla, E.R. et al. (2010). Gene Regulatory Models for Plant Development and Evolution. In: Pua, E., Davey, M. (eds) Plant Developmental Biology - Biotechnological Perspectives. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02301-9_1

Download citation

Publish with us

Policies and ethics